I travel frequently to Cognac, and I am a big fan of La Ribaudière in Bourg Charante. I typically order the menu, which was 54 euros for dinner in November. I have also heard that Château de l'Yeuse is good. This past trip I had lunch at Le Bistro des Quais, which was quite nice.
My favorite place to stay is Domaine de l’Echaissier.